Question: The sum of two angles is $88^\circ$. Angle 2 is $80^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 88}$ ${y = 3x-80}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-80}$ for $y$ in the first equation. ${x + }{(3x-80)}{= 88}$ Simplify and solve for $x$ $ x+3x - 80 = 88 $ $ 4x-80 = 88 $ $ 4x = 168 $ $ x = \dfrac{168}{4} $ ${x = 42}$ Now that you know ${x = 42}$ , plug it back into $ {y = 3x-80}$ to find $y$ ${y = 3}{(42)}{ - 80}$ $y = 126 - 80$ ${y = 46}$ You can also plug ${x = 42}$ into $ {x+y = 88}$ and get the same answer for $y$ ${(42)}{ + y = 88}$ ${y = 46}$ The measure of angle 1 is $42^\circ$ and the measure of angle 2 is $46^\circ$.